Within the human body, most cells interact with their neighboring cells and with their extracellular matrix to establish a unique organization.
These cell-cell and cell-matrix interactions form a complex network of mechanical, biological and chemical signals which play a significant role in cell physiology [1]}, [2]}, [3]}, [4]}.
The study of cellular interactions provides a significant insight towards a better understanding of many biological processes such as tumor growth [5]}, [6]}, tissue spreading [7]}, [8]}, [9]}, [10]}, biofilm formation [11]}, [12]}, [13]} and wound healing [14]}, [15]}.
Although there exist numerous contributions on experimental methods to examine cellular interactions and their final outcomes [16]}, [17]}, [18]}, [19]}, [20]}, there are still certain details and information that remain hard to assess.
Examples of such details include the exact relation between the interactions and individual cell's adhesion properties, or the speed at which sorting between the cells occurs.
Clearly, determining the relationships between all the problem variables via conducting experiments is an arduous and time consuming task.
Theoretical approaches, however, provide a valuable alternative as they do not suffer from such limitations and facilitate parametric studies.
Mathematical modeling allows us to quantify parameters such as local speeds, fluxes and their rates of change in a natural way.
They also enable us to investigate the effects of interactions between cells of different types or to allow the cell properties to vary independently of one another.
Given these benefits, mathematical modeling proves to be an inclusive and efficient alternative for analyses of cellular interactions [21]}.
